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This invention relates to a technique to accurately assess the performance of non-deadtime compensated (e.g., proportional-integral-derivative or PID) Controllers. Specifically, the technique accounts for the reduction in achievable performance of these controllers due to the lack of deadtime compensation as compared to minimum variance controllers.
Non-deadtime compensated controllers, in particular PID controllers, are the prevalent form of controllers in many industrial applications. It is necessary to evaluate the performance of these controllers for the following reasons:
1. Analyze current controller shortcomings.
2. Explore future control opportunities.
3. Benchmark the current controller quality.
Performance of these controllers is largely defined as how well the controller maintains the process measurement at setpoint. A method for evaluating this question is the subject of this patent.
The simplest and most direct technique of determining controller performance is to calculate the variance between the measurement (yt) and the setpoint (SPt), i.e.,       σ    2    =            1      n        ⁢                  ∑                  t          =          1                n            ⁢              xe2x80x83            ⁢                        (                                    y              t                        -                          SP              t                                )                2            
The subscript t on all variables indicates that the value is for the time t (txe2x88x921 refers to the value at the previous time, etc). While simple to claculate, this measure has the extreme disadvange that it is dependent on the level of disturbances or setpoint changes (i.e., only reason why the setpoint would not equal the measurement is due to disturbance/setpoint changes), and is thus more an indication of the disturbance/setpoint spectrums than the capabilities of the controller.
For this reason Harris et al. (1992) defined a Performance Index measure ( ) that is independent of the disturbance/setpoint change spectrum and can be readily used to determine the actual performance of the controller. This measure compares the performance of the controller to a theoretical Minimum Variance controller (i.e., the best physically realizable linear controller, which does contain a deadtime compensator), and can be calculated from routine operating data. This latter property is a strong advantage, as no plant tests are required to determine the measure. This measure is common in industry and is often referred to as the Harris Performance Index. This technology described in this patent is a modification or extension to the Harris Performance Index to account for one of the limitations of non-deadtime compensated Controllers.
The Minimum Variance controller referenced by Harris et al. (1992) employs a model of the process in the following form:                               y          t                =                                                                              ω                  ⁡                                      (                    B                    )                                                  ⁢                                  B                  b                                                            δ                ⁡                                  (                  B                  )                                                      ⁢                          μ              t                                +                                                    θ                ⁡                                  (                  B                  )                                                                              φ                  ⁡                                      (                    B                    )                                                  ⁢                                  ∇                  d                                                      ⁢                          a              t                                                                    xe2x80x83                ⁢                  (          1          )                                        =                                            G              p                        ⁢                          μ              t                                +                                    G              d                        ⁢                          a              t                                                                    xe2x80x83                ⁢                  (          2          )                    
This is standard time series notation for process transfer functions, and says that the output yt is a function of the input ut and an independent white noise input at. B is the backwards shift operator, i.e. Byt=ytxe2x88x921. The input passes through a linear discrete process model, while the noise input passes through a linear discrete disturbance model.
This is all the information required to design a Minimum Variance Controller. While these controllers provide the best possible control, they are never implemented as they result in excessive input movement and are sensitive to model mismatch. They do, however, represent an upper bound on the performance of a system.
A minimum variance controller contains deadtime compensation, that is, the current output is based on past outputs at least as far back in time as the process deadtime. In general, these controllers are of the form:
ut=xcex1(B){tilde over (y)}t+xcex2(B)utxe2x88x921xe2x80x83xe2x80x83(3)
xe2x80x83=Gc{tilde over (y)}txe2x80x83xe2x80x83(4)
The order of the polynomial xcex2(B) is at least b, where b is the deadtime divided by the sampling time. Here {tilde over (y)}t is the deviation from setpoint, i.e., {tilde over (y)}t=SPxe2x88x92yt. The process input ut is therefore a function of the current and past process output deviations from setpoints {tilde over (y)}t and the past b process inputs utxe2x88x921,utxe2x88x922, . . . utxe2x88x92b.
In contrast, the output for a PID controller is calculated as:
ut=utxe2x88x921+xcex10{tilde over (y)}7+xcex11{tilde over (y)}txe2x88x921+xcex12{tilde over (y)}txe2x88x922xe2x80x83xe2x80x83(5)
Which indicates that the current controller output is a function of only the last controller output and the last few measurements. PID and other non-deadtime compensated controllers will result in degraded control for process with significant deadtime as they lack a memory term for control actions past the most recent one.
This invention addresses the above limitation of PID controllers and their assessment using the standard Harris Index. There is no method to differentiate in the Harris Index the contribution due to detuning and equipment limitations and that due to the restricted structure of the PID controller itself. The basis of the performance measure in this invention is an optimal non-deadtime compensated (or PID) controller, and thus this index will give an indication of detuning or equipment limitations exclusively.
Of concern in the present invention is to determine the performance of a non-deadtime compensated controller (i.e., proportional-integral-derivative (PID)) using normal closed-loop operating data.
It is, therefore, a feature of the present invention to provide a method to determine the performance of a PID Controller, or of any controller that lacks deadtime compensation.
It is, also, a feature of the present invention that it only requires normal operating data to determine the controller performance.
Yet another feature of the present invention is that the performance measure adequately reflects the lack of deadtime compensation of PID controllers.
It is, also, a feature of the present invention that it has the same range and interpretation as the Harris Controller Performance Index.
Additional features and advantages of the invention will be set forth in part in the description which follows, and will in part be apparent from the description, or may be learned from practice of the invention. The features and advantages of the invention may be realized by means of the combinations and steps pointed out in the appended claims.
To achieve the objectives, features, and advantages, in accordance with the purpose of the invention as embodied and broadly described herein, a method to determine the performance of a non-deadtime compensated controller is provided. This performance measure accounts for the lack of deadtime compensation of these controllers, which is not accounted for in other metrics used to calculate controller performance, and may be calculated using only on-line data and an estimate of the deadtime.
Accordingly, besides the objects and advantages of the non-deadtime compensated Controller Performance Index described in my above patent, several objects and advantages of the present invention are:
a) to assess the performance of a non-deadtime compensated controllers using only normal operating data;
b) to obtain a measure that has the same interpretation and range of the Harris controller performance index;
c) to obtain a measure that accounts for the lack of deadtime compensation of the controller.